School Science Lessons
Topic 06
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6.0 Measurement
Table of contents
See: Measurement, (Commercial)
14.0 Measurement (Primary)
6.2.0 Measurements, Different measurements, billion, trillion Accuracy and error
6.3.01 Angle, angular Ångström unit, A
6.3.05 Area (shape)
35.3.01 Assay value of precious metals Astronomical unit, au
12.1.05 Atmospheric pressure, Conversions between units
3.2.1 Avoirdupois weight, English and United States weights and measures
9.145 Brix, sucrose concentration
36.42.2 Cable, Knots, Latitude, nautical mile, knots, log, logbook
19.8.0 Common measures
38.7.00 Computers
3.4.2 Construct a rectangle from parts of a square Draft (draught) of a ship Distilled water, deionized water
36.36.0 Earth, effect of the earth's motion Errors, Accuracy and error
6.4.0 Errors, theory of errors, addition of uncertainties Electric current, ampere
3.6.0 Estimating
36.42.2 Latitude, nautical mile, knots, log, logbook
3.4.1 Fifth field (map colouring topology)
4.1.0 Graphs henry, H, Inductors in AC circuits (SI unit) Kilogram, mass
Knots, nautical mile
36.42.2 Latitude, nautical mile, knots, log, logbook Length Luminous intensity, candela, cd Mass, kilogram
2.0.0 Mathematics, graphs
KB kilobyte
MB megabyte
3.5.4a Measuring cups, jugs 5.1.0 Mole, amount of substance
5.1.1 Mole, Prepare molar solutions
Nautical mile, knot
6.14.0 Oven temperatures
12.1.01 Pressure definitions, Millibar, 1 millibar = 100 pascal (Pa) Radioactivity, radiation units, curie
3.7.0 Ratio and proportion, concentration
6.3.0 SI, International system of units, [Système international d'unités (French)] Temperature, Celsius scale, Kelvin scale, Fahrenheit scale Time
6.3.07 Tonnage, displacement Triple point and ice point temperatures of water
6.3.03 Velocity (speed)
Viscosity, poise
6.3.06 Volume Weight, standards of weight

2.0.0 Mathematics, graphs
See: Mathematics (Commercial)
See Part 11 websites, Mathematics and computers
Arithmetic mean (png file)
2.0.5 Conic sections, parabola, ellipse, hyperbola (GIF file)
6.15.4 Ellipse, draw an ellipse
6.15.3 Fractions
Geometric mean (png file)
2.0.2 Golden mean (GIF file)
2.0.2a Golden mean and point of balance
4.1.1 Graphs
4.2.2 Graphs, Variation of temperature in water with time
Greek alphabet
2.0.8 Mathematics for science experiments (GIF) Möbius strip Newton, The newton, symbol N
2.0.6 Parabola equation (GIF file)
6.15.0 Perfect numbers
6.15.01 Prime numbers
3.2.2 Rank scaling tables
6.13.0 Roman numerals
2.0.7 Scale of a map (GIF file)
Symbols Table of numerals adding vertically / horizontally / diagonally to 33
6.15.1 Tests for divisibility

6.3.0 SI, International system of units, [Système international d'unités (French)]
See: Measurement (Commercial)
1.0 SI, The 7 base units
3.0 SI derived units
3.1 Other derived units, based on SI
3.5 Units used with SI units (Area, Mass, Pressure, Volume)
3.6 SI, CGS and FPS conversion, metric conversion
3.5 SI prefixes, Decimal fractions and multiples Weight, standards of weight
3.2.4 Apothecaries' weights
3.2.1 Avoirdupois weight
3.2.2 Carat Mass, kilogram
9.235 Measure your weight
3.2.3 Troy weight
6.12.0 Weights of one matchbox full of fertilizer Accuracy and error
6.4.0 Errors, theory of errors, addition of uncertainties
6.4.1 Significant figures and standard form, scientific notation
6.4.2 Order of magnitude (nearest power of ten, factor or factors of ten)
6.4.3 Order of accuracy
6.4.1a Standard form, scientific notation
6.4.4 Use measuring instruments, micrometer screw gauge, vernier calipers Factors that affect readings, obtain data from the equipment Relative positions between measured object and equipment Reaction time of the equipment Line of vision Record measurements in tables Table of numerals adding vertically or horizontally or diagonally to 33
3.2.2 Rank scaling tables

3.7.0 Ratio and proportion, concentration
6.6.3 Surface / volume ratio, small block and large block.
Relative size of electron, atom, molecule, cell, man and woman, earth.
3.7.1 Concentration, parts per million (PPM) Pi, π
3.7.2 Rate of reaction
3.7.3 Degrees proof, proof spirit
2.0.2 Golden mean (GIF file) Non-SI units
3.5.3 American liquid measures, US measures, United States weights and measures, volume to liquid Ångström unit Astronomical unit, au (non-SI unit)
3.5.2 British liquid measures, imperial measures
(fl. oz. = imperial fluid ounce) (ounce Latin: uncia, 12th part of a pound)
3.9.0 CGS units (centimetre, gram, second)
3.13.1 Einstein was right, e = mc2
3.13.0 Energy conversion KJ, MJ, kWh, therm, BTU, calorie, horsepower
3.11.0 Imperial units used in land surveying (1 hectare = 10 000 m2, 1 km = 1 000 m)
36.42.2 Knots, Latitude, nautical mile, knots, log, logbook
36.14.2 Light year, parsec, minute of arc, arc second (non-SI units)
3.5.7 Micron, µ (mu)
3.10.0 m.k.s. units Quark
3.12.0 SI, c.c.s. and f.a.s. conversion, metric conversion
3.5.1 Spoon volume United States lineal weights and measures United States surface (land), weights and measures
Viscosity, poise

6.3.01 Angle, angular
17.5.8 Angle of repose of an inclined plane Angle, radian, degree, arc second
3.33 Angle tube syringe, Collect gas with an angle tube syringe (GIF)
15.3.0 Angular acceleration, tangential acceleration, α t, and centripetal acceleration, α c
18.3.4 Angular momentum, Conservation of angular momentum
18.3.3 Angular momentum, Transfer of angular momentum
15.0.4 Angular velocity, ω, radians, rad
18.3.0 Angular velocity, Rotational dynamics, rotational motion Line of vision Radians
2.0.1 Right-angled triangle (GIF)

6.3.03 Velocity (speed)
14.1.01 Scalars and vectors
28.1.1 Speed of light, C
3.13.1 Speed of light, C, Einstein was right, e = mc2
4.24 Speed of reaction, catching the ruler
26.5.0 Speed of sound (Velocity of sound in  gases, liquids, and solids)
14.1.0 Velocity and speed

6.3.05 Area (shape)
3.4.0 Area, square metre (m2), hectare Aspect ratio
6.6.3 Surface / volume ratio of soil particles

6.3.06 Volume
See: Volume (Commercial)
3.5.3 American liquid measures, US measures, United States weights and measures, volume (liquid)
3.5.2 British liquid measures, imperial measures (fl. oz. = imperial fluid ounce)
3.5.4 Common measures
1.29 Measuring cylinders / graduated cylinder
3.5.1 Spoon volume
6.6.3 Surface / volume ratio of soil particles
3.5.0 Volume (vol.), cubic metre (m3)
2.1.6 Volume of liquid (meniscus diagram) Length Ångström unit, A Astronomical unit, au
36.42.2 Latitude, nautical mile, knots, log, logbook
3.3.0 Length (l), kilometre (km), metre (m) Metre (meter) (m) Time
See: Time, (Commercial) Second Leap second The "present" Temperature Temperature, Celsius scale, Kelvin scale, Fahrenheit scale Celsius scale Fahrenheit scale Kelvin scale, absolute zero
6.14.0 Oven temperatures Triple point and ice point temperatures of water.

3.2.1 Avoirdupois weight, English and United States weights and measures
The imperial unit ounce may be a measure of mass or volume
1 avoirdupois weight pound (lb) = 16 ounces (oz.).
All chemicals were sold by avoirdupois weight.
(Latin: pondus (weight), 12 ounces of pure silver, 240 pennies, so cash to the value of 20 shillings sterling, symbol lb
(Latin: libra pondo (libra, scale, pondo, by weight)
Table 3.2.1 1 Avoirdupois weight
pound ounce drachm, dram grain (Troy) g
1 16 256 7 000 453.60
. 1 16 437.5 28.35
. . 1 27.34 1.771 845

A fluid dram is 1 ⁄ 8 of a fluid ounce, i.e. 3.696 mL USA and 3.551 mL UK.
In Scotland, a dram is a small volume of Scotch whisky.

3.2.2 Carat
35.20.18 Carat, Gold, Au, natural gold, medical use (Geology)
For precious stones, 1 carat is about 1 / 142 of an ounce, formerly 3.17 grains, now standardised at 0.20 grams.
For gold, a carat is a ratio of 1 / 24.
Purity of gold is measured in carats.
24 carat gold is pure gold.
22 carat gold is 22 parts pure gold and 2 parts copper or other metal alloy.
14 carat gold is 14 parts pure gold and 14 parts copper or other metal.
The official mark stamped on gold and silver objects after being assayed is the hall mark (from Goldsmith's Hall, London).
For gold, the standard mark is a crown in England for 22 and 18 carat gold followed by the number of carats in figures.
Lower standards of gold have the number of carats in figures without the crown.

3.2.3 Troy weight
Gold is still sold in troy ounces, as were precious metals.
1 troy weight pound, lb = 12 troy ounces.
1 grain = 6.479 × 10-5 kg.
Table 3.2.3 Troy weight
Latin denarius, penny
pound ounce pennyweight, Dwt grain g
1 12 240 5 760 373.24
. 1 20 480 31.10
. . 1 24 1.56

3.2.4 Apothecaries' weight, English and United States weights and measures,
English and United States weights and measures
Apothecaries' measures were formerly used in pharmacy and were usually adopted in formulas.
1 fluid ounce = 8 drachms = 489 minums.
The pound, ounce and grain are the same as in Troy weight.
In UK, the fluid drachm (fluidrachm) = 3.55 mL.
Table 3.2.4 Apothecaries' weight
pound ounce drachm scruple grain g


1 12 96 288 5 760 373.24
. 1 8 24 480 31 103
. . 1 3 60 3 888
. . . 1 20 1.30
. . . . 1 0.06

3.3.0 Length (l), the kilometre (km), metre (metre, m)
See: Measurement (Commercial)
A metre is the length of a path travelled by light in a vacuum during a time interval of 1 / 299 792 458 of a second.
calipers, Vernier calipers, Vernier scale (Pierre Vernier 1580-1637), calipers are for measuring internal and external diameters.
Gauge, feeler gauges, micrometer screw gauges, to find the thickness of one sheet of paper in a pile
Rule, measuring timber for carpentry, tape measure, dressmaking measurements:
circumference of the chest / waist / hips,
trundle wheels to measure the length of a crooked path
1 kilometre, 1 km = 1 000 metres (originally, a line from the north pole to the equator through Paris was thought to be 10, 000 km)
1 decimetre, 1 dm = 0.1 metre
1 centimetre, 1 cm = 0.01 metre
1 millimetre, 1 mm = 0.001 metre
1 micrometre (or micrometer), 1 µ m = 1 × 10-6 metre, one millionth of a metre, micron
1 nanometre, 1 nm = 10-9 metre, one billionth of a metre (10 angstroms) (formerly 1 millimicron)
1 angstrom, A
1 picometre, 1 pm = 10-12 metre. Ångström unit, A
3.5.7 Micron, µ (mu)
One ångström unit, symbol A = 10-10 metre (one hundred-millionth of a centimetre), previously used as unit of measurement of
wavelength, but nowadays use nanometre.
(Note: 1 nm = nanometre = 10 Angstrom units = 10-9 m.).
The unit, named after A. J. Ångström, Sweden (1814-1874), is still used in crystallography and to measure wavelengths of the
electromagnetic spectrum. Astronomical unit, au
One Astronomical unit = the mean distance between the Earth and the Sun, 149 597 871 km, but taken as 1.496 × 108 km,
(93 million miles).
It is used as a convenient way to measure distance in the solar system. United States lineal weights and measures
foot (singular) feet (plural), yard (Old English: gerd, stick, rod) (mile: Latin: mille, 1 000, 1 000 paces, about 1 680 yards),
(inch from ounce Latin: uncia, 12th part of a foot)
Table United States lineal weights and measures
mile furlong rod yard foot inch
or "
1 8 320 1 760 5 280 63 360
1 40 220 660 7 920
- - 1 5.5 16.5 198
- - - 1 3 36
- - - - 1 12 Relative positions between measured object and equipment +
When you read on a scale with a measured object directly touching with the equipment, be careful as their relative position will
probably affect precision of your readings.
For example, if you measure temperature of liquid by a thermometer, you must immerse completely the measuring bulb in the liquid as
you take readings. Reaction time of the equipment
Some equipment reacts to measured quantities very quickly, such as meters for measuring electricity.
However, some equipment needs a certain reacting time, such as a mercury thermometer.
So you must take readings after the equipment stabilizes.
Even with equipment that reacts quickly you need to pay attention to such problems, e.g. when measuring electric potential, be certain
that the pointer no longer moves before you read from the scale. Line of vision
The angle between your line of vision and the object referred to can cause errors.
Your eye should be at right angles to the scale and directly opposite the part of the scale you are reading.
Reading a scale from the left side or the right side or above or below are all wrong, because they result in parallax error. United States surface (land) weights and measures
1 square foot = 144 square inches
1 square yard = 9 square feet
1 square rod = 30.25 square yards
1 square rood = 40 square rods
1 acre = 4 square rods
1 square mile = 640 acres = 2 560 roods = 102 400 rods = 3 097 600 square yards = 27 878.400 square feet
Table United States surface (land) weights and measures
acre rood rod yard foot

1 4 160 4 840 43 560
. 1 40 1 210 10 890
. . 1 30.25 272.25
. . . 1 9 Record measurements in tables
Set up a table vertically if there is a possibility of additional requiring some extra space.
Include a title and table number on the top of a table to state what data the table contains.
The first column should contain data for the independent variable rather than the dependent variable.
The weight is the independent variable because you decide its values, usually before doing the experiment.
The increase in length of spring is the dependent variable because it depends on the weight added.
Express all data in standard form.
Increase in length of spring.
(Original length = 28.0 cm)
Table Record measurements in tables
Length of spring
Increase in length
0.49 (0.5 kg) 32.8 4.8
0.98 (1 kg) 36.3 8.3
1.47 (1.5 kg) 39.4 11.4
1.96 (2.0 kg) 41.9 13.9 Aspect ratio
Aspect ratio is the proportion between width and height, W:H format, e.g. for HD television channels the aspect ratio =16:9, 1.77:1.
Check the aspect ratio on your television set.
Each paper size in the A series of International Standard (I.S.O.), paper sizes is half the area of the next biggest sheet, half as wide,
but same length, so 2 A4 sheets side to side = 1 A3 sheet.
If length = L and width = W, L /W = sqrt 2 = 1.41, the aspect ratio for the A series of paper sizes.
So one sheet of A3 can be reduced to one sheet of A4, with the photocopier control panel set to 71%, approximately 1/sqrt 2.
Similarly, for enlargements, the control panel is set to 141%.
This aspect ratio allows exact reductions or enlargement, but in USA and Canada, the American National Standards Institute (ANSI),
uses two different aspect ratios in photocopiers.
A series
A1 paper 841 mm X 1189 mm, A2 half that, A3 half that, A4 half that, A8
ANSI E paper 34 inches X 44 inches. Table of numerals adding vertically or horizontally or diagonally to 33, the traditional age of Jesus when he died.
Table Numerals adding vertically or horizontally or diagonally to 33
1 14 14 4
11 7 6 9
8 10 10 5
13 2 3 15 Möbius strip
1. A Möbius strip is a two-dimensional surface with only one side.
It can be constructed in three dimensions as follows.
Take a rectangular strip of paper and join the two ends of the strip together so that it has a 180 degree twist.
It is now possible to start at a point A on the surface and trace out a path that passes through the point which is apparently on the other
side of the surface from A.
2. Cut a strip of paper 2 cm wide on writing paper with lines on only one side.
Hold the strip by each end and half twist it, i.e. twist it by 180o.
Note that you could twist it to the left or to the right.
Use adhesive tape to stick the two ends together to make a loop.
Hold the paper strip against the point of a pencil then draw a line along the middle of the strip without taking the pencil off the paper.
Keep drawing the line until you get back to where you started.
Examine both sides of the strip of paper and note that you have drawn on both sides of the paper.
Use sharp scissors to cut along the line.
Note that you now have a new loop twice as long as the original loop.
3. Using a longer strip of writing paper 2 cm wide, repeat the above experiment with a full twist, 360o.
Again cut along the a line in the middle of the strip to produce two separate loops, the same size as before, but linked together like a link
is in a chain.
4. This loop was discovered by August Ferdinand Mobius and Johann Benedict Listing in 1858, but the ancient Greeks may have
known it.
The mobius strip seems to be useless, but it has been used in car fan belts, conveyor belts and continuous loop recording tapes to
double the playing time.
5. Möbius joke: Q. "Why did the chicken cross the Möbius strip?" A. "To get to the same side".

3.4.0 Area, square metre (m2) hectare
1 km2 = 1 square kilometre = 1000 m × 1000 m × 1000 m.
It does not mean 1000 square metres.
Land: 100 metres (m) × 100 metres (m) = 10 000 square metres (m2) = (104 m2) = 1 hectare (ha) = 2.471 acre = 107 639 ft2
Imperial units used in land surveying (1 hectare = 10 000 m2, 1 km = 1 000 m)
Area of cloth for a dress, area of a bolt of cloth, floor cover, area of a fitted carpet.
Irregular shape area, use of graph paper.
Regular shape area, square, rectangle, circle
Area of the top of a matchbox: 20 cm2
Area of a square = length l2
Area of a rectangle = length l × width w
Area of a parallelogram = length l × vertical height / 2
Area of a circle = π × r2
cu. = cubic
Surface area of a sphere = 4π × r2
Volume of a sphere = 4 / 3 π × r3.

3.4.1 Fifth field
See diagram 3.4.01: The four fields
See the diagram of the four fields labelled A, B, C and D.
Each of the fields has a common boundary with all the other fields.
Can you draw a fifth field, E, which has a common boundary with all the other fields, A, B, C, and D?
It cannot be done!
You cannot draw a fifth field of any side or shape with common sides with four other fields.
So if you have to add colour to the different States in a map of the United States of America, you need no more than four different
colours to ensure that no two States with a common border have the same colour.

3.4.2 Construct a rectangle from parts of a square
See diagram 3.4.2: Square and rectangle
Draw the square in the diagram and draw the same lines to divide the square into four pieces.
Note the angle a.
Use scissors to cut out the four pieces.
Rearrange the four pieces to form a rectangle.
Why the increase in area?
Tan angle a in the square = 3/8 = 0.375.
Tan angle a in the square = 5/13 = 0.3846
So the pieces really do not fit together to form a rectangle.

3.5.0 Volume (vol.) cubic metre (m3)
See diagram 2.1.6: Liquid volume
Volume in a measuring cylinder, meniscus
Volume of a bucket, fish tin, coconut, tablespoon, teaspoon, cooking oil for food, of agricultural chemical to be used on a farm
Volume of water used at home or school, reading a water meter
Volume of petrol (gasoline) used by a motor vehicle
Volume of irregular shapes, volume of small quantity of sand or glass beads.
Displaced volume, overflow vessels
Volume of regular shapes, a cube, a block, cylinder, sphere, cone
Volume of gas used at home or school, reading a gas meter
Volume, solid: 1 centimetre (cm) × 1 centimetre (cm) × 1 centimetre (cm) = 1 cubic centimetre (1 cc, 1 cm3) = 1 millilitre, 1 mL
[millilitre mL (SI unit), also milliliter, ml, mℓ] (a thousandth of a litre of capacity)
1 cubic decimetre, 1 dm3 = 1 litre, 1 L = 1000 mL = 1000 cm3 = 1000 cc
Volume, liquid: 1 000 millilitres = 1 litre (L)
Mole, 1 mole, 1 M = 1 mole per cubic decimetre = 1mole per litre = 1 mol. L-1.

3.5.1 Spoon volume
1 tablespoon (tbsp) (spoon to serve with, the biggest spoon):
15 mL (most countries) to 20 mL (Australia) (0.5 fl oz)
1 dessertspoon (the spoon you eat with) = 10 mL (2 teaspoons)
1 teaspoon, tsp. (the smallest spoon)
1 teaspoon, tsp., UK = 4.5 to 5 mL (0.2 fl oz) (UK 4 mL) (1 fluid dram)
1 teaspoon, tsp., US = 1 / 3 tablespoon, 1 / 6 U.S. fl. oz, 1 / 48 of a cup,
1 / 768 of a U.S. liquid gallon (1 / 3 of a cubic inch, cu. in.)
1 teaspoon, tsp., US = 5 mL (for US food labels))
1 measuring spoon for medicines and some fertilizers = 5 mL
(1 salt spoon, saltspooon = ¼ teaspoon).
1 tablespoon, tbsp. = 3 teaspoon, tsp.

3.5.2 British liquid measures, imperial measures (fl. oz. = imperial fluid ounce)
These measures were usually adopted in formulas.
1 fluid ounce = 28.42 mL (0.96 US oz)
1 imperial pint = 568.3 mL (20 fl oz)
1 quart = 1140 mL (40 fl oz) (38.5 US oz)
1 imperial gill = 0.132 L (5 fl oz)
1 imperial gallon = 4.54 609 litres, 4.55 L
1 fluid drachm = 60 minims
1 fluid ounce = 8 fluid drachms
1 pint = 20 fluid ounces
1 gallon = 8 pints.
1 hogshead (of beer) = 54 imperial gallons (245.48 litres).

3.5.3 American liquid measures, US measures, United States weights and measures, volume to liquid
1 liquid US pint = 473.1 mL (473.179 cc) (16 fl oz)
1 dry US pint = 550.6 mL (19 fl oz)
1 US fluid ounce = 29.56 mL (29.574 cc)
1 US gill = 0.118 L
1 US gallon = 3.79 L (3 785.435 cc)
1 pint = 4 gills
1 quart = 2 pints
1 gallon = 4 quarts (231 cubic inches)
pt. pint
qt. quart
gal. gallon.

3.5.4 Common measures
See: Measurement, (Commercial)
See: Measuring Cylinders, (Commercial)
3.5.4a Measuring cups, jugs spoons
1 barleycorn, 1 / 3 inch, 0.84667 cm (old British unit)
1 barrel, bbl., of crude oil = 42 US gallons, = 34.97 Imperial gallons (about 159.1 litres)
1 barrel (petroleum) = 35 imperial gallons (about 159 L)
1 barrel (beer cask) = 32 imperial gallons
1 cubic inch = 16.38 cubic centimetres
1 cubit = (English cubit 46 cm) (Roman cubit 44 cm) (Egyptian cubit 53 cm) (Hebrew 56 cm), traditional from the tip of the elbow
to the tip of the
longest finger)
1 cup, cupful = 284 mL
1 cup, teacup (the cup you use with a saucer) = 200 - 250 mL
(1 / 4 cup of butter, half fill a cup with water, add butter until water rises to the 3 / 4 level)
1 dash = what you pick up between your thumb and first two fingers
1 drachma = 1 / 8 oz
1 ell = 45.5 cm (English), 37 cm (Scotch), 54 cm (French) (cloth measure from elbow to finger tips)
1 English wine bottle 750 mL
1 fluid ounce = 29.57 millilitres, mL
1 Foolscap printing paper = 13.5 × 17 inches
1 Foolscap writing paper = 13.25 × 16.5 inches
1 glass, wine glass = 1 / 4 cup
1 hair breadth = 1 inch / 48
1 human's body temperature 37oC (Celsius
1 hundredweight, British hundredweight, 112 pounds, 1 Cwt., 1 / 20 ton,
("long hundredweight"), 50.80 kg
1 hundredweight, US hundredweight, cwt, 100 pounds (lb) ("short hundredweight"), 45.36 kg
1 hundredweight, metric hundredweight 50 kg
1 Imperial fluid ounce = 28.42 cc
1 jeroboam = 4 English wine bottles = 4 × 262 / 3 fluid ounces
1 jerrican = 4½ gallons (used for military fuel)
1 jigger = 1.5 fl oz
1 journey-weight of gold = 15 pounds troy (701 sovereigns)
1 kati, caddy = 1 lb, 5 oz, 2 dr, weight still used in Malaysia
(1 kati said to be 12 / 16 British pound in Hong Kong)
1 league, about 2-4 miles
1 matchbox volume = 25 mL, Area of the top of a matchbox = 20 cm2
1 magnum = 2 English wine bottles (2 "reputed" quarts)
1 nail = formerly a weight of 8 pounds or a length of 2.25 inches
1 peck = 2 dry gallons, a quarter of a bushel
1 penny weight = 1 / 20 fl. oz
1 pinch = what you pick up between your thumb and first two fingers
(½ pinch = to what you can pick up between your thumb and one finger)
1 pipe = 105 gallons of wine
1 quart (liquid) = 0.9463 litre
1 quarto sheet of paper, folded twice to give 4 leaves, 8 pages, about as high as wide
1 quintal, q, 100 kg = 220.5 pounds
1 rehoboam = 6 English wine bottles
1 US bushel = 35.24 litres
1 US liquid gallon = 3.785 litres
1 US short ton = 0.9072 tonne
1 US long ton = 1.016 tonne.

3.5.4a Measuring cups, jugs spoons
See: Measuring Cylinders, (Commercial)
Jug plastic, translucent, graduated with multiple measuring units, 1000 mL
Measuring cylinders / graduated cylinder: 1.29
Plastic measuring spoon set, 1.25 mL, 2.5 mL, 5 mL, 20 mL, set / 4
Plastic measuring cups, ¼, 1 / 3, ½, 1 cup, set / 4
Polypropylene beakers, opaque, unsuitable for heating, graduated with multiple measuring units, 1000 mL. Draft (draught) of a ship
The draft is the vertical distance between the waterline and the bottom of the hull or keel.
The draft usually varies along the length of the ship.

3.5.7 Micron, µ (mu)
The term "micron" was discarded by international agreement, but it was still used in industry and some sciences.
Then it was accepted again, because "micrometre" was confused with the "micrometer", a measuring device containing a fine pitched
micron, µ (non-SI unit) = 1 micrometre, µm (British English) (1 micrometer, USA), a millionth of a metre
1 micrometre (1.000 µm) = 1.000 × 10-6 metre (m), one millionth of a metre, micron
(Micrometre is used to measure wavelength of infrared radiation.)
1 nanometre (1 nm) = 10-9 metre, one billionth of a metre, (10 angstroms) (formerly 1 millimicron)
1 millimicron (mµ) = 1 / 1000 of a micron = 10-9 metre = 10-3 micrometre = 10 Angstrom =
SI unit nanometre (nm) (USA nanometer) (one billionth of a metre)
1 angstrom = 1.0 × 10-10 metres
(millisecond and microsecond are non-SI units).

3.6.0 Estimating
Estimating of parameters, prediction, size perception, relative size
Estimating height of people, tree, a house, bridge, mountain
Estimating distance from the roadside, of the car ahead.

3.7.1 Concentration, parts per million (ppm)
Concentration is the quantity of dissolved substance to quantity of solvent.
Dilution is the volume of solvent in which a measured amount of solute is dissolved.
Different ways of expressing concentration, e.g. ppm, % weight for weight (w/w), % weight for volume (w/v).
Parts per million by mass (ppm, milligrams per kilogram, 0.0 001%) = about a grain of sugar in a cup of tea.
Parts per million, ppm, 1 ppm = 1 mg per litre.
Parts per million, ppm, usually refers to ppm by weight 1g solute per 1, 000, 000 g solution  =
0.001 g per 1, 000 g solution =
1 mg solute per 1 kg solution
If aqueous solution, where concentration of solute is so low that assume solution density = 1.00 g / mL,
then ppm = 1 mg of solute per litre of solution.
So using this assumption, convert ppm in mg / Litre to molarity in mol / Litre.
If x ppm of Ca2+ ions (atomic weight of calcium = 40.8),
then x ppm = x mg Ca2+ / Litre of solution = 0.00x g / Litre, 0.00x / 40.08
= mol / Litre.

3.7.2 Rate of reaction
For many chemical reactions, but not all, increasing the concentration of reactants increases the rate of reaction.
The rate constant, k, is the constant for a given reaction at a given temperature.
H2 (g) + I2 (g) --> 2HI (g)
rate = k [H2 (g)] [I2 (g)], where [H2 (g)] = concentration of hydrogen gas
If x = any substance, [x] = concentration of x.
If in a chemical reaction, [x] is doubled and the rate of reaction remains constant, then the rate of reaction is independent of [x].
If in a chemical reaction, [x] is doubled and the rate of reaction doubles, then the rate of reaction = k[x].

3.7.3 Degrees proof, proof spirit
Proof is a standard of strength of distilled alcoholic liquors.
Proof spirit contains, in Britain 49.28% alcohol (ethanol) by weight, 57.10% by volume, relative density 0.920 at 10.6oC (formerly
specific gravity of 12 / 13 at 51oF) in USA 50% by volume at15.6oC.
This standard is quoted as 100 degrees of proof, 100o.
If a spirituous liquor is p% overproof (above standard strength, contains more alcohol than proof spirit)
it contains as much alcohol in 100 vol as in 100 + p vol of proof spirit.
20o proof = 0.2 × 57.1% alcohol = 11.42% ALC / VOL, e.g. white wine.
Concentration of alcohol can also be measured with a hydrometer.
Formerly, proof spirit was an alcoholic beverage that, if poured over gunpowder and ignited, would ignite the gunpowder.
If the gunpowder did not ignite, the spirit was "under proof".

3.9.0 The CGS. units (centimetre, gram, second)
Table 3.9.0 The CGS. units (centimetre, gram, second)
Quantity CGS Unit
Length centimetre 1 cm = 10-2 m
Mass gram 1 g = 10-3 kg
Area cm2 1 cm2 = 10-4 m2
Volume cm3 1 cm3 = 10-6 m3
Density g cm-3 1 g cm-3 = 10-3 kg m-3

3.10.0 The m.k.s. units
The metric system of units based on metre, kilogram, second.
Also, the electrical unit was the ampere and magnetic constant was 4 pi × 10-7 Hm-1 (henry = H, now SI unit of inductance).

3.11.0 Imperial units used in land surveying (1 hectare = 10, 000 m2, 1 km = 1, 000 m)
Table 3.11.0 Imperial units used in land surveying
Imperial Metric Imperial Metric
1 square mile 259.0 hectare (ha) 1 link 0.201 168 m (exact)
1 square mile 2.589 988 km2 1 foot 0.3 048 m (exact)
1 acre 4 046.856 m2 1 mile 1.609 344 m (exact)
1 acre
0.4047 hectare (ha)
1 perch
25.2 929 m2
1 rood 1 011.714 m2 0.03 954 perch 1 m2

1 square centimetre, cm2 = 0.1550 square inch (in2)
1 square inch = 645.2 square mm
1 square metre (m2) = 10.76 square feet
1 square metre (m2) = 1.196 square yard
1 square metre (m2) = 0.0002471 acre (ac)
1 square mile = 1 U.S. "section"
1 hectare (ha) = 2.471 acre = 107 639 ft2
1 hectare (ha) = 0.00386 square mile
1 yard (yd) = 0.9 144 metre (m)
1 square foot = 0.92 903 square metre.

3.12.0 SI, CGS and FPS conversion, metric conversion
CGS = centimetre, gram, second
FPS = foot, pound, second
MK or MESA = metre, kilogram, second (ampere).

Table 3.12.0 SI, CGS and FPS conversion, metric conversion
Physical quantity CGS.
FPS unit
length, metre, meter (m) 1 centimetre (cm) = 0.3937 inch (in)
1 inch (in) = 25.4 millimetre (mm)
" 1 metre = 3.2808 feet (ft)
1 foot (ft) = 0.3048 metre (m)
1 metre (m) = 1.094 yard (yd)
1 yard (yd) = 0.9144 metre (m)
" 1 kilometre (km) = 0.6213 mile
1 mile = 1.6093 kilometre (km)
mass, kilogram (kg) 1 gram (g) = 10-3 kilogram (kg)
1 gram (g) = 0.0353 ounce (oz.)
1 kilogram (kg) = 2.205 pounds (lb)
1 ounce (oz) = 28.35 gram (g)
1 pound (lb) = 0.4536 kilogram (kg)
1 tonne (t) = 1.102 US short ton, 2000 pounds (lb)
1 tonne (t) = 0.9843 US long ton, 2, 205 pounds (lb)
1 US hundredweight (cwt) = 100 pound (lb)
1 US cwt = 45.36 kilogram (kg)
1 US short ton = 0.9072 tonne (t)
1 US long ton = 1.016 tonne (t)
volume, litre, liter (L)
1 cm3 = 10-6 m3
1 litre (L) =10-3 m3
1 millilitre (mL) = 1 cm3
1 cubic centimetre (cc) = 0.0610 cubic inch
1 millilitre (mL) = 0.3382 fluid ounce
1 litre (L) = 0.2642 US liquid gallon
1 litre (L) = 0.02838 US bushel
1 cubic inch = 16.38 cubic centimetre (cc)
1 fluid ounce = 29.47 millilitre (mL)
1 US liquid gallon = 3.785 litre (L)
1 US bushel = 35.24 litre (L)
1 quart (liquid) = 0.9463 litre (L)
1 g cm-3 = 10-3 kg m-3
1 kilogramme / hectolitre = 0.7770 pound / US bushel

1 pound / US bushel = 1.287 kg / hL
velocity or speed 1 cm s-1 = 10-2 m s-1 .
" 100 km / hour 62.5 miles / hour
dyne, 1 dyne = 10-5 newton (N) .
1 dyne cm2 = 10-1 pascal (Pa) .
" 1 bar = 105 pascal (Pa) 1 bar = 750.07 mm Hg
" millibar = 100 pascal (Pa) .
energy, work (J = joule) 1 erg = 10-7 joule (J)
power (W = watt)
1 erg S-1 = 10-7 watt (W) 1 horsepower (hp) = 745.7 watt (W)
1 poise (P) = 10-1 NM-2s .
0oC (Celsius) = 32oF (Fahrenheit)
100oC = 212oF
32oF (Fahrenheit) = 0oC (Celsius)
212oF = 100oC
thermal energy
1 calorie (cal) = 4.186 joule (J) British thermal unit, 1 BTU = 1.055 × 103 J

3.13.0 Energy conversion kJ, mJ, kWh, therm, Btu, calorie, horsepower
1 kilowatt (kW) = 1.341 horsepower (hp)
1 kilojoule (kJ) = 0.948 British Thermal Unit (Btu)
1 megajoule (mJ) = 948 Btu = 0.28 kWh = 0.37 horsepower hours
1 joule (J) = 0.239 calories (cal)
1 therm = 100 000 British Thermal Unit (BTU) = 106 mJ
1 British Thermal Unit (BTU) = 1.055 kilojoule
1 kilowatt hour, kilowatt-hour (kWh) = 3 412 Btu = 3.6 mJ
1 calorie (cal) = 4.186 J (if International Table calorie), however, the 15oC calorie = 4.1855 J
1 horsepower (hp) = 746 watts, 0.7457 kilowatt
1 horsepower hour (hph) = 2.69 mJ watt, W.

3.13.1 Speed of light, C, Einstein was right, e = mc2
Albert Einstein's celebrated formula e = mc2 has finally been corroborated, thanks to a mighty computational effort by French, German
and Hungarian physicists.
A brain power consortium led by Laurent Lellouch, of France's Centre for Theoretical Physics, using some of the world's most
powerful supercomputers, has set down the calculations for estimating the mass of protons and neutrons, the particles at the nucleus of
According to the conventional model of particle physics, protons and neutrons comprise smaller particles known as quarks, which are
bound by gluons.
The odd thing is the mass of gluons is zero and the mass of quarks is 5 per cent.
Where is the missing 95 per cent?
The answer, according to the study published in US journal Science, comes from the energy from the movements and interactions of
quarks and gluons.
In other words, energy and mass are equivalent, as Einstein proposed in his "Special Theory of Relativity" in 1905.
The e = mc2 formula shows that mass can be converted into energy, and energy can be converted into mass.
By showing how much energy would be released if a certain amount of mass were to be converted into energy, the equation has been
used many times, most famously as the basis for atomic weapons.
Resolving e = mc2 at the scale of sub-atomic particles in equations called quantum chromodynamics to has been difficult.
"Until now, this has been a hypothesis," France's National Centre for Scientific Research said proudly in a statement.
"It has now been corroborated for the first time."
For those keen for more, the computations involve "envisioning space and time as part of a four-dimensional crystal lattice, with
discrete points spaced along columns and rows".
AAP (Australian Associated Press) The Australian (newspaper), November 22-23, 2008.
Einstein wrote: "If a body emits the energy L in the form of radiation, its mass decreases by L/V2.
Here it is obviously inessential that the energy taken from the body turns into radiant energy, so we are lead to the more general conclusion.
The mass of a body is a measure of its energy content; if the energy changes by L, the mass changes in the same sense by L/9 x 1020
if the energy is measured in ergs and the mass in grams."
In these units, speed of light = 3 X 1010 cm per second, and speed of light squared = 9 X 1020.
Substitute E for L, and c for V, then mass, m, decreases by E/c 2, E= mc 2. Quark
The name of the fundamental building block of matter, the quark, comes from the novel "Finnergans Wake" by James Joyce was given
this name by Murray Gell-Mann.
It is generally pronounced "qwork" to rhyme with "pork".

6.2.0 Different measurements, billion, trillion
Traditional counting units, a score, a dozen (doz.), common units, market units
Units and scale divisions, analogue units, digital units
b bit
B byte 
KB kilobyte
1 kB = 1 000 bytes = 103B
1 kB = 1 024 bytes = 210B
MB megabyte
1 MB = 1 0002 B = 106 B = 1 000 000 bytes
1 MB = 1 0242 B = 220 B = 1 048 576 bytes
Cardinal numbers, cardinal numerals, positive whole numbers, 1, 2, 3. . .
Hundred, 102, one hundred, 100
Thousand, 103, one thousand, 1 000
Million, a thousand thousand, one million, 1 000 000
Billion, a million million, 1012 in UK, but a thousand million, 109, in USA, now most popular use in the world
Trillion, a million million million, 1018, in UK, but a million million, 1012, in USA, now most popular use in the world
Googol, ten raised to the hundredth power, 1 then 100 zeroes, 10100.
The term "googol" is not in formal mathematics use.
The name "googol" is said to be invented by Milton Sirotta, 9 years old nephew of US mathematician Edward Kasner.
"Google", proprietary name of internet search engine, also transitive verb meaning to use Google to find information.
The name of the search engine "Google" is an accidental misspelling of "googol".

6.3.07 Tonnage, displacement
Measurement of the volume of a boat for registration and fees, e.g. Panama canal fees
Gross tonnage, GT = KV where V= total volume in cubic metres and K = 0.2 + 0.02 log10V
Net tonnage, NT, is the total cargo space
The displacement, the volume of the hull below the waterline × specific gravity of water, is expressed in metric tons (not tonnage!). Length, metre
A metre is the length of a path travelled by light in a vacuum during a time interval of 1 / 299 792 458 of a second.
1 metre, m (SI unit)
1 centimetre, cm, also centimeter
1 kilometre, km, also kilometer
1 millimetre, mm, also millimeter
Originally, 1 metre = 1 / 10 000 000 of the meridian through Paris, between the North Pole and the Equator. Mass, kilogram
See: Mass, (Commercial)
See 36.10.2: Mass, inertial mass and gravitational mass
The kilogram is the base unit of mass.
Originally, the gram was intended to be the mass of a cubic centimetre of pure water at 4oC, but the gram was later defined as one
thousandth part of a kilogram.
So the standard of mass is now the kilogram.
A kilogram is the mass of the international prototype kilogram kept in Sevres, France, as a 90% platinum and 10% iridium cylinder at
the International Bureau of Weights and Measures.
A proposed alternative definition, called the Planck value is that a kilogram is such that the Planck constant is exactly
6.6 260 693 × 10-34 joule seconds.
Weight: 1000 grams (g) = 1 kilogram (kg), 1000 kg = 1 metric tonne (t)
MT metric ton t, T  metric ton, kilogram, kg (SI unit of mass) also kilogramme, kilo, microgram, µg, milligram, mg. Distilled water, deionized water
See: Distilling (Commercial)
1. Distilled water, as sold by Sigma-Aldrich
Distilled water, CAS Number 7732-18-5, Empirical Formula (Hill Notation) H2O, Molecular Weight 18.02
Beilstein Registry Number 2050024, EC Number 231-791-2, MDL number MFCD00011332, refractive index n20 / D 1.34(lit.)
bp 100 °C (lit.), density 1.000 g / mL at 3.98 °C (lit.), [conductivity 0.05 μS / cm (microSiemens / cm)]
2. Water deionized, deionized water, as sold by Sigma-Aldrich, exactly the same as above, except it also includes the
following information:
conductivity ≤4.3 μS / cm at 20 °C
3. Deionized water really has no ions, except for H+ and OH- ions, but it may be not as pure as distilled water if it contains organic
Low cost: Purchase distilled water at supermarkets or garages.
For many chemistry and physics experiments, cheaper demineralized water is a suitable substitute for the dearer distilled water. Second
See: Time (Commercial)
A second is the time equal to the duration of 9 192 631 770 cycles of oscillation (periods of the radiation) corresponding to the
transition between the two hyperfine levels of the ground state of the caesium 133 atom.
Before 1956, the mean solar day was 24 hours, at 60 minutes per hour, and 60 seconds per minute =
84, 400 seconds.
60 seconds = 1 minute
60 minutes = 1 hour
24 hours = 1 day
7 days = 1 week,
365 days = 1 year, 366 days = 1 leap year
10 years = 1 decade
100 years = 1 century
1000 years = 1 millennium
a.m. (ante meridiem) = morning
p.m. (post meridiem) = afternoon
1.00 p.m. = 1300 hours. Leap second
See: Time (Commercial)
ABC / Reuters, Posted Sun Jul 1, 2012 1:26pm AEST (Australia)
An extra second has been added to the world's atomic clocks in an adjustment to keep them in step with the slowing rotation of the Earth.
The so-called "leap second" was added to electronic clocks at midnight universal time on Saturday.
At that time, atomic clocks read 23 hours, 59 minutes and 60 seconds before they moved on to Greenwich Mean Time.
Super-accurate atomic clocks are the ultimate reference point by which the world sets its wrist watches.
But their precise regularity, which is much more constant than the shifting movement of the Earth around the sun that marks out our days
and nights, brings problems of its own.
If no adjustments were made, the clocks would move further ahead and after many years the sun would set at midday.
Leap seconds have a similar function to the extra day in each leap year, which keeps the calendar in sync with the seasons.
The last so-called leap seconds happened in 2008, 2005 and 1998.
Adjustments to atomic clocks are more than a technical curiosity.
A collection of the highly accurate devices are used to set Coordinated Universal Time, which governs time standards on the world
wide web, satellite navigation, banking computer networks and international air traffic systems.
There have been calls to abandon leap seconds, but a meeting of the International Telecommunications Union, the UN agency
responsible for international communications standards, failed to reach a consensus in January.
Opponents of the leap second want a simpler system that avoids the costs and margin for error in making manual changes to thousands
of computer networks.
Supporters argue it needs to stay to preserve the precision of systems in areas like navigation.
A decision is not urgent.
Some estimate that if the current arrangement stays, the world may eventually have to start adding two leap seconds a year.
But that is not expected to happen for another hundred years or so. The "present"
See: Time (Commercial)
Archaeologists define "the present" at 1 January 1950, a date before nuclear explosions contamination of the Earth.
So an event said to occur "10, 000 years ago" occurred 10, 000 years before 1 January 1950. Temperature, Celsius scale, Kelvin scale, Fahrenheit scale
See: Thermometers (Commercial)
See diagram 23.7.00: Celsius temperature scale
The temperature of a body is its hotness or coldness with reference to a standard of comparison.
Temperature varies with the amount of heat energy in the body.
To convert between Fahrenheit scale and Celsius scale:
C = (F-32) X 5/9. Fahrenheit scale
See: Thermometers (Commercial)
The Fahrenheit temperature scale (Gabriel Daniel Fahrenheit 1686 - 1736), has graduations on the thermometer based on a lower fixed
point of 32oF, the freezing point of water, and an upper fixed point of 212oF, the boiling point of water.
So the fundamental interval is 180 Fahrenheit degrees,180oF.
The Fahrenheit scale is still used in USA.
To convert the Fahrenheit scale to the Celsius scale (F-32) / 9 = C / 5.
So 68oF = 20oC. Celsius scale
See: Thermometers (Commercial)
The Celsius temperature scale, proposed in 1724 (Anders Celsius 1701-1744), has graduations on the thermometer based on a lower fixed
point of 0oC, the freezing point of water, and an upper fixed point of 100oC, the boiling point of water.
So the fundamental interval is 100 Celsius degrees.
The Celsius scale was formerly called the centigrade scale, "100 steps"scale.
Some people still incorrectly quote temperatures in "degrees centigrade".
C = "Celsius" NOT "Centigrade".
The unit "degree Celsius" is equal to the unit "kelvin", and a temperature interval may also be expressed in "degrees Celsius".
To convert the Fahrenheit scale to the Celsius scale (F-32) / 9 = C / 5.
So 68oF = 20oC
The Celsius and Fahrenheit scales have the same value at -40oC, or -40oF.
Human body temperature = 37oC (Celsius), or 98.6oF (Fahrenheit). Kelvin scale, absolute zero
See: Thermometers (Commercial)
The Kelvin scale (Lord Kelvin 1824 - 1907) is based on the idea of absolute zero.
Molecular motion, heat, approaches zero, the null point, as the temperature approaches -273.15oC.
One kelvin degree, 1 K = 1 Celsius degree, 1oC.
Absolute zero = -273.15oC = 0K, not "degree Kelvin".
To convert the Celsius scale to the Kelvin scale, add 273.15.
For example, 0oC = 273.15 K, 100oC = 373.15 K, and 10oC = 283.15 K.
So this scale begins at absolute zero and increases in kelvins.
The Kelvin scale is the preferred scale for scientific experiments.
The temperature, kelvin, is the fraction 1 / 273.16 of the thermodynamic temperature of the triple point of water.
Proposed alternative definition of temperature, kelvin:
The kelvin is such that the Boltzmann constant is exactly 1.3806505 ×10-23 joules per kelvin.
An approximate value of absolute zero may be obtained by plotting pressure versus temperature and extrapolating the line produced to
zero pressure.
Submerge the bulb of a pressure gauge successively in boiling water (100°C), ice water (0°C), and dry ice in alcohol (-78.5°C) and
record the corresponding pressure indicated by the gauge.
Table Equivalent temperatures in different scales (F-32) / 9 = C / 5 | K = C + 273.15
Kelvin Celsius Fahrenheit
Absolute zero 0oK -273oC -459oF
Freezing point of water 273oK 0oC 32oF
Boiling point of water 373oK 100oC 212oF

9.145 Brix, sucrose concentration
See: Refractometers YHequipment, for testing brix, (Commercial)
One degree Brix, 1Bx = 1 g sucrose in 100 g as % w/w, as used in fruit juice, honey and wine industries.
Brix meters calculate mass fractions and give the value as Bx.
A sucrose solution with specific gravity 1.040 at 20oC is 9.99325 Bx or 9.99249%.